Which decimal is equivalent to $\dfrac{1}{3}$ ? Choose 1 answer: Choose 1 answer: (Choice A) A $0.\overline{13}$ (Choice B) B $0.\overline{3}$ (Choice C) C $1.\overline{3}$ (Choice D) D $3.\overline{3}$
Explanation: $ \dfrac{1}{3}$ represents $1 \div 3 $. ${3}$ ${1}$ ${0}$ ${0}$ ${.}$ ${.}$ $\text{Write in a decimal and a zero.}$ $\text{How many times does }3\text{ go into }{10}\text{?}$ ${3}$ ${9}$ $-$ ${1}$ ${10}\div3={3}\text{ with a remainder of }{1}$ $\text{How many times does }3\text{ go into }{10}\text{?}$ ${0}$ ${0}$ ${3}$ ${9}$ $-$ ${1}$ ${10}\div3={3}\text{ with a remainder of }{1}$ $\text{How many times does }3\text{ go into }{10}\text{?}$ ${0}$ ${0}$ ${3}$ ${9}$ $-$ ${1}$ ${10}\div3={3}\text{ with a remainder of }{1}$ $\text{How many times does }3\text{ go into }{10}\text{?}$ ${0}$ ${0}$ ${3}$ ${9}$ $-$ ${1}$ ${10}\div3={3}\text{ with a remainder of }{1}$ $\text{How many times does }3\text{ go into }{10}\text{?}$ ${0}$ ${0}$ ${3}$ ${3}$ ${9}$ $-$ ${1}$ ${1}$ ${10}\div3={3}\text{ with a remainder of }{1}$ Notice how the decimal is repeating and will continue to repeat as we bring down more zeros. So $\dfrac{1}{3}$ is equivalent to $0.\overline{3}$.